ASTROPHYSICAL BLACK HOLES

SOME HISTORY Escape velocity v u 2 = 2 GM/R Earth v esc = 11 km/s Jupiter v esc = 60 km/s Sun v esc = 600 km/s Moon v esc = 2 km/s J. Michel P. Laplace r(v esc =c) = ? r = 2 G M/v esc 2

r g = 2 G M/c 2 r g gravitational radius Schwarzshild’s radius (r S ) radius of event horizon r g = 3 M/M SUN km Term „black hole” introduced by J. Wheeler in 1964 For neutron star: r g ≈ 4.2 km r NS ≈ 10 km

From 7 orbits: M BH = (3.7 ± 0.2) x 10 6 M SUN (Ghez & al., 2005) Star S0-16 approaches the focus of the orbit to a distance of ~ 45 A.U. (~ 6 light hours or ~ 600 R S )

From new analysis of orbit of S0-2 (astrometry & RVs from Keck 10 m) : M BH = (4.5 ± 0.4) x 10 6 M SUN independently D = 8.4 ± 0.4 kpc (Ghez & al., 2008)

HOW ARE BLACK HOLES CREATED ? They are evolutionary remnants of massive stars

FINAL PRODUCTS OF STELLAR EVOLUTION ● low mass stars (M ≤ 10 M SUN ) ● massive stars (10 M SUN ≤ M ≤ 20 M SUN ) WHITE DWARFS M ~ 0.2 ÷ 1.3 M SUN, R ~ km NEUTRON STARS M ~ 1 ÷ 2 M SUN, R ~ 10 km BLACK HOLES M ≥ 3 M SUN observed M ~ 4 ÷ 33 M SUN ● very massive stars (M ≥ 20 M SUN )

X-RAY SKY (UHURU, 1977)

Black holes can grow up i.e. increase their masses. This is done by attracting the matter from the neighbourhood (BH acts as a „vacuum cleaner”) or by mergers. In this way intermediate mass BHs (thousands solar masses) and then supermassive black holes (millions to billions solar masses) are created.

● STELLAR MASS BHs ● SUPERMASSIVE BHs ● INTERMEDIATE MASS BHs 3 CLASSES OF BHs

HOW DO WE KNOW THAT BLACK HOLES ARE THERE ?

ALL THESE ARGUMENTS PROVIDE ONLY CIRCUMSTANTIAL EVIDENCE HARD EVIDENCE COMES ONLY FROM DYNAMICAL ESTIMATE OF THE MASS OF THE COMPACT OBJECT

UPPER MASS LIMIT for NSs ● THEORY ● OPPENHEIMER-VOLKOFF MASS: M OV ≈ 1.4 ÷ 2.7 M SUN depending on the equation of state FOR EXTREME EQUATION OF STATE : P=ρc 2 (assuming only GR and causality): M OV ≈ 3.2 M SUN for non-rotating NS M OV ≈ 3.9 M SUN for maximally rotating NS

● OBSERVATIONS ● BINARY RADIO PULSARS M NS ≈ 1.33 ÷ 1.44 M SUN (until recently) ● BINARY X-RAY PULSARS M NS ≈ 1.1 ÷ 1.9 M SUN (large errors)

NEW DETERMINATIONS OF NS MASSES ● PSR J B M = ± M SUN (Lyne & al., 2004) ● PSR J M = 1.67 ± 0.01 M SUN (Champion & al., 2008)

NGC 6440B After ~1 year timing this pulsar, we have obtained a good measurement of the rate of advance of periastron. If fully relativistic, this implies a total system mass of ~2.92 ± 0.25 solar masses! The companion has likely only ~0.1 solar masses. Median of probability for pulsar mass is 2.74 solar masses. There is a 99% probability of mass being larger than 2 solar masses, 0.1% probability of having a “normal” mass. Is this a super-massive neutron star? From: Freire et al. (2008a), ApJ 675, 670

PSR J Freire, 2009

CONFIRMED BHs IN XRBs Name P orb Opt. Sp. X-R C M BH /M sun Cyg X-15 d 6 O9.7 Iab pers μQ 20 ± 5 LMC X-31 d 70 B3 V pers 6 ÷ 9 LMC X-14 d 22 O7-9 III pers 10.9 ± 1.4 SS d 1 ~ A7 Ib pers μQ 16 ± 3 LS d 906 O7f V pers μQ 2.7 ÷ 5.0 XTE J d 817 B9 III T μQ 6.8 ÷ 7.4 GX d 76 F8-G2 III RT μQ ≥ 6 GRO J h 09 M2 V T 4 ± 1 A h 75 K4 V RT 11 ± 2 GRS h 96 K8 V T 4.4 ÷ 4.7 XTE J h 1 K7-M0 V T 8.5 ± 0.6 GS h 4 K0-5 V T 7.0 ± 0.6

CONFIRMED BHs IN XRBs (cont.) Name P orb Opt. Sp. X-R C M BH /M sun GS d 54 G0-5 III T > 7.8 ± 0.5 4U d 12 A2 V RT 8.5 ÷ 10.4 XTE J d 55 K3 III RT μQ 10.5 ± 1.0 XTE J h 63 K4 V T μQ 4.0 ÷ 7.3 GRO J d 62 F3-6 IV RT μQ 6.3 ± 0.5 4U h 54 K5 V T 5.7 ÷ 7.9 GRO J h 7 M0-5 V T > 4.9 XTE J h1 6 ~ G5 T 8 ÷ 10 GRS d 5 K-M III RT μQ 14 ± 4.4 GS h 26 K5 V T 7.1 ÷ 7.8 GS d 46 K0 IV RT 10.0 ÷ 13.4

INTERMEDIATE MASS BHs ● range of masses: ~ 10 2 ÷ 10 4 M SUN TWO CLASSES OF CANDIDATES: ● ULXs ● globular clusters

GLOBULAR CLUSTERS Do some of them contain IMBHs ? Some of them, probably, yes. How many – it remains an open question.

Brightness profiles r c /r h clusters with IMBHs have expanded cores (r c /r h > 0.1)

Trenti (2006) considered a sample of 57 old globular clusters For at least half of them, he found r c /r h ≥ 0.2 IMBHs necessary !

Velocity dispersion correlates well with M BH (IMBH or SMBH)

Gebhardt et al., 2002

STRONGEST CANDIDATES ● [ G1 M BH ~ M SUN Gebhardt et al., 2005 ] ● M15 M BH ~ M SUN Gerssen et al., 2003 ● ω Cen M BH ~ M SUN Noyola et al., 2006

Are ULXs BH binaries (IMBH binaries) ? Some of them – yes! The term „ULXs” is probably a sort of an umbrella covering several different classes of objects One of them is, most likely, a class of XRBs containing IMBHs

L x ≈ (2.4 ÷ 16) x erg/s (if L x = L Ed, M x = 150 ÷ 1000 M sun ) QPOs: & Hz M x ~ 200 ÷ 5000 M sun probably accreting from a ~ 25 M sun giant filling its Roche lobe P orb ≈ 62 d M 82 X-1 In dense stellar cluster MGG-11, 7 ÷ 12 Myr old (Patruno et al., 2006)

SUPERMASSIVE BHs ● range of masses: 3x10 5 ÷ 6x10 10 M SUN

DIFFERENT WAYS OF DETERMINING M BH ● Kepler’s law ● individual stars ● water masers ● M BH –M bulge relation ● „reverberation” (also based on Kepler’s law) ● „variance” (X-ray variability)

Kepler’s law – water masers

NGC 4258 M BH = (3.9 ± 0.1) x 10 7 M SUN (Herrnstein et al., 1999)

M BH -M bulge relation Hoering & Rix, 2004

● highest masses TON 618 M BH ≈ 6.6 x M SUN 5 AGNs with M BH > M SUN ● lowest masses NGC 4395 M BH ≈ 3.6 x 10 5 M SUN Sgr A * M BH ≈ 4 x 10 6 M SUN

A binary composed of two supermassive BHs Quasar OJ287 P orb ≈ 12 yr e = 0.66 M 1 ≈ 18 bilions of solar masses M 2 ≈ 100 milions of solar masses optical flashes twice per orbital period strong GR effects

Emission of gravitational waves is very efficient. In a few thousand years one black hole will crash into another.

SPINS of BHs Spins of accreting BHs could be deduced from: 1. X-ray spectra (continua) require the knowledge of M BH, i & d 2. X-ray spectra (lines) require the proper substraction of continuum 3. kHz QPOs require the knowledge of M BH and the proper theory of QPOs

Specific angular momentum for circular orbits

X-RAY SPECTRA Zhang et al. (1997): GRO J a* = 0.93 GRS a* ≈ 1.0 Gierliński et al. (2001): GRO J a* = 0.68 ÷ 0.88 McClintock et al. LMC X-3 a* < 0.26 (2006, 2009): GRO J a* = 0.65 ÷ U a* = 0.70 ÷ 0.85 LMC X-1 a* = 0.81 ÷ 0.94 GRS a* > 0.98

SPECTRAL LINES MODELING THE SHAPE OF Fe Kα LINE Miller et al. (2004): GX339-4 a* ≥ 0.8 ÷ 0.9 Miller et al. (2005): GRO J a* > 0.9 XTE J a* > 0.9 Miller et al. (2002): XTE J a* ≈ 1.0

Miller (2004)

Reis et al. (2008) determined the spin of BH in GX (from RXTE & XMM): a* = ± 0.02 at 90 % confidence (!) r in = r g at very high state r in = r g at low/hard state Miller et al. (2008) did this from Suzaku & XMM: a* = 0.93 ± 0.05 NEW ERA OF PRECISION

SUMMARY OF SPIN DETERMINATIONS FROM Fe Kα LINE Cyg X-1 a* = 0.05 (1) 4U a* = 0.3 (1) SAX J a* = 0.2 ÷ 0.8 SWIFT J a* = 0.61 ÷ 0.87 XTE J a* = 0.75 (9) XTE J a* = 0.76 (1) XTE J a* = 0.79 (1) GX a* = 0.94 (2) GRO J a* = 0.98 (1) Miller et al., 2009

GRO J ± ± ± 20 XTE J ± ± ± 20 H ± ± 3 GRS ± 1 14 ± ± ± 2 4U ± 5 XTE J ± 4 9 ± 1 XTE J ± 1.5 kHz QPOs Name ν QPO [Hz] M BH [M SUN ]

MASS ESTIMATES BASED ON SPINS PARAMETRIC EPICYCLIC RESONANCE THEORY (Abramowicz & Kluzniak, since 2001) ● simple resonance (2:1, 3:2 etc.) ● „humpy” resonance

a ≈ 0.7 ÷ 0.99 a* ≈ 0.7 ÷ 0.99

BHs SPINS (summary) (1) GRS has a rotation close to nearly maximal spin ( a* >0.98) (2) several other systems (GX 339-4, LMC X-1, GRO J , XTE J , XTE J , XTE J and SWIFT J have large spins (a* ≥ 0.65) (3) not all accreting black holes have large spins (robust results a* < 0.26 for LMC X-3 and a* ≈ 0.05 for Cyg X-1)

New VLBI observations at 1.3 mm (Doeleman et al., 2008) permitted us to see (for the first time) the structures on the scale of the event horizon!

Doeleman et al., 2008

The diameter of the event horizon of Sgr A* is ~ 20 μas (for d = 8 kpc) The apparent size for a distant observer should be (due to light bending) ~ 52 μas for non-rotating BH or ~ 45 μas for maximally rotating BH The measured size (major-axis) of Sgr A* is μas the emission from Sgr A* is not exactly centered on a BH (jet?, disc?)

Images calculated for RIAF disc emission close to the event horizon (Yuan et al., 2009) indicate that disc is highly inclined or Sgr A* is rotating fast.

Yuan et al., 2009